A381844 Quotients of A380487.
1, 3, 5, 7, 11, 19, 23, 34, 91, 105, 209, 221, 231, 385, 399, 429, 481, 609, 665, 715, 805, 897, 1001, 1105, 1430, 1729, 1870, 2046, 2233, 2261, 3094, 3230, 3553, 3565, 3774, 4278, 4862, 4921, 4945, 5270, 5358, 5365, 6409, 6670, 7429, 7462, 7657, 7990, 8041, 8569
Offset: 1
Keywords
Examples
1 is a term because rad(2)/sopf(2) = 2/2. 3 is a term because rad(30)/sopf(30) = 30/10. 5 is a term because rad(70)/sopf(70) = 70/14.
Links
- Robert Israel, Table of n, a(n) for n = 1..168
Programs
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Maple
f:= proc(n,m) local q,S; S:= numtheory:-factorset(n); q:= convert(S,`*`)/convert(S,`+`); if q::integer and q > m then q else 0 fi; end proc: m:= 0: R:= NULL: count:= 0: for n from 2 while count < 50 do v:= f(n,m); if v > 0 then m:= v; R:= R,v; count:= count+1; fi; od: R; # Robert Israel, Apr 30 2025 -
PARI
lista(nn) = my(m=0, list=List()); for (n=2, nn, my(f=factor(n)[,1], q=factorback(f)/vecsum(f)); if ((denominator(q) == 1) && (q>m), listput(list, q); m=q);); Vec(list); \\ Michel Marcus, Mar 29 2025
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Sage
def sopf(n): return sum(set(prime_factors(n))) def rad(n): rad = 1 for p in set(prime_factors(n)): rad *= p return rad def output(limit=39): results = [] n = 2 result = 0 while len(results) < limit: sopf_n = sopf(n) rad_n = rad(n) if rad_n % sopf_n == 0 and result < rad_n / sopf_n: result = rad_n / sopf_n print(result, end=', ') n += 1 return output()
Comments